1. Field of the Invention
The invention relates to a moirxc3xa9 method for measuring the distortion of an optical imaging system and a system suitable for carrying out the method.
2. Description of the Related Art
Optical imaging systems are employed in numerous fields of engineering and research that impose increasingly stringent demands on their imaging quality. An example is photolithographic fabrication of semiconductor devices and other types of microdevices, where submicrometer-range structures are created using high-performance projection lenses. In semiconductor-device fabrication, imaging optics that have intolerably high distortion may, for example, cause defects in integrated circuits that will reduce yields of good integrated circuits and thereby increase fabrication costs. Such projection lenses have elaborate optical trains having large numbers of lenses that usually make it impossible to derive their optical characteristics from theoretical computations. The optical characteristics of their imaging systems must thus be reliably measured. The stringent demands on the imaging accuracies of their optical imaging systems impose even more stringent demands on the accuracies of the testing methods employed for checking their imaging systems. In particular, high-precision measurements of their distortion are absolutely essential.
Numerous testing methods for measuring the distortion of optical systems are based on exploitation of the moirxc3xa9 effect. For example, analyzing moirxc3xa9 fringe patterns created by linear grids in order to determine lens distortion along an image direction of a two-dimensional image field, in which a so-called xe2x80x9cobject gridxe2x80x9d that has a transparent substrate bearing a large number of parallel, opaque lines that form an object pattern is arranged in the object plane of the imaging system to be tested, is known. An image grid having an image pattern similar to the object pattern is arranged in the lens"" image plane. Both grids are arranged such that they are orthogonal to the optical axis of the imaging system. The object pattern and the image pattern are adapted to suit one another such that a moirxc3xa9 pattern exhibiting moirxc3xa9 fringes is created when the object pattern is imaged onto the image pattern using the imaging system.
Creation of a moirxc3xa9 fringe pattern may be achieved by accurately matching the ratio of the grid constants of the image grid and object grid to the lens"" prescribed magnification. Rotating one of these grids with respect to the other grid about the optical axis will then create a moirxc3xa9 pattern consisting of bright and dark fringes running nearly orthogonal to the grid lines on the object and image grids. The number of pairs of fringes created is equal to the number of grid lines of one grid that intersect a grid line of the other grid. A moirxc3xa9 fringe pattern may also be created by slightly altering the grid constants of the object grid and image grid, for example, altering them by a few percent, duly allowing for the image magnification involved. Moire methods of this type are described in, for example, U.S. Pat. No. 5,767,959, or U.S. Pat. No. 5,973,773, which has a substantially identical content.
Lens distortion, which is usually small compared to the grid constant of the image grid, may, for example, be determined by phase shifting, in which various moirxc3xa9 fringe patterns, each of which is created by progressively shifting grids with respect to one another parallel to their grid lines by a fraction of their grid period, are recorded by a camera. A periodic change in intensity is observed at each image location during this phase shifting. The relative phase of these signals at various measurement locations is a measure of lens distortion orthogonal to the grid lines.
The aforementioned method allows determining distortion along a single image direction, namely, that orthogonal to the grid lines, only. If distortion components along other image directions are to be determined, the lens is normally rotated about its axis through, for example, 90xc2x0, before any further measurements are performed, which requires employment of a mechanically complex measurement setup.
European Patent No. EP 0 418 054 describes another moirxc3xa9 method that allows initially determining the distortion components along an image direction and then determining the distortion components along an image direction orthogonal thereto in two consecutive steps, where, in the case of one embodiment, the object grid bears a two-dimensional object pattern in the form of a cross-hatched pattern. The image grid, on the other hand, is one-dimensional and has a set of parallel lines. Moreover, the projection lens whose distortion is to be measured is equipped with a translatable pupil filter that may be used to transmit either the first-order diffracted reflections in the x-direction or those in the y-direction and block all other reflections. Switching between the measurement directions involves both translating the pupil filter and rotating the image grid through 90xc2x0. This system thus allows dispensing with rotating the lens. However, it necessitates an intervention into the projection lens in order to incorporate a suitable pupil filter and construction of an elaborate mount for the image grid that will allow rotating the image grid through 90xc2x0.
It is one object of the invention to provide a moirxc3xa9 method and an associated measuring system that will allow rapid, reliable, two-dimensional distortion measurements, i.e., distortion measurements along several, differing, image directions, while maintaining the mechanical requirements imposed on the measurement system low. It is another object to provide a moirxc3xa9 method and measuring system that allow simultaneously measuring the distortion components of an imaging system along two mutually orthogonal image directions.
As a solution to these and other objects the invention provides a moirxc3xa9 method for measuring the distortion of an optical imaging system comprising:
arranging an object grid having a two-dimensional object pattern in an object plane of the imaging system; arranging an image grid having a two-dimensional image pattern in an image plane of the imaging system;
wherein the object pattern and image pattern are adapted to suit one another such that a two-dimensional moirxc3xa9 fringe pattern may be created when the object pattern is imaged onto the image pattern using the imaging system;
imaging the object pattern onto the image pattern in order to create a two-dimensional moirxc3xa9 fringe pattern;
detecting the two-dimensional moirxc3xa9 fringe pattern;
determining at least one first distortion component and at least one second distortion component from the two-dimensional moirxc3xa9 fringe pattern, where the first distortion component is correlated to a first image direction of an image plane and the section distortion component is correlated to a second image direction transverse to the first image direction.
An associated system for making two-dimensional measurements of both distortion components comprises an object grid having a two-dimensional object pattern arranged in an object plane, an image grid having a correspondingly adapted two-dimensional image pattern arranged in an image plane, devices for imaging the object pattern onto the image pattern and for detection the two-dimensional moirxc3xa9 fringe pattern created, and a device for determining the first and second distortion components from the moirxc3xa9 fringe pattern.
To be interpreted as a xe2x80x9ctwo-dimensional patternxe2x80x9d in the sense of this application are both the pattern itself, which is extended in two dimensions, and the pattern""s spectrum, which is also extended in two dimensions, i.e., is modulated in two dimensions. In other words, a xe2x80x9ctwo-dimensional patternxe2x80x9d refers to both the field and the pupils.
A preferred setup provides that the object grid will be irradiated using an illumination device and that radiation modified by the object pattern will be imaged onto the image grid by the imaging system. Suitable grids may be, e.g., transmission gratings, phase gratings, or reflection gratings, depending upon the application involved. A preferred device for detecting the two-dimensional moirxc3xa9 fringe pattern is thus a two-dimensional detector, for example, a detector equipped with a CCD-chip, for detecting superimposed images of the object pattern and image pattern. Although other imaging optics are preferably incorporated between the image grid and object grid, they may be omitted.
In principle, the method according to the invention allows determining two mutually orthogonal, or, in general, several, distortion components of a lens correlated to differing image directions from a single, detected, two-dimensional moirxc3xa9 fringe pattern. It is thus highly unlikely that temporal variations of the measurement setup, which can be critical, particularly in the case of phase-shift measurements, will cause erroneous measurement results.
The object pattern and image pattern are preferably present in the form of a superposition of two mutually orthogonal line gratings, e.g., a cross-hatched pattern or a checker-board pattern. Rotating the image grid relative to the object grid, or vice versa, preferably about the optical axis of the measuring system, will then lead to creation of two-dimensional moirxc3xa9 fringe patterns that are largely periodic along two mutually orthogonal image directions, and from which the distortion components correlated to the first and second image directions may be extracted. Fringe width and fringe spacing may be adjusted by adjusting the rotation angle, which will allow, for example, adapting them to suit the resolving power of a camera provided for the purpose of recording the moirxc3xa9 fringe pattern.
Analysis of the information contained in the two-dimensional moirxc3xa9 fringe pattern, from which, e.g., distortion components along two mutually orthogonal directions may be derived, may be complicated by crosstalk among moirxc3xa9 components. In order to arrive at unambiguous segregations of the imaging information that are uniquely correlated to image directions, a Fourier transform of the moirxc3xa9 fringe pattern may be initially computed in order to determine a frequency spectrum along the first and/or second image direction. Subsequent filtering of a range about a fundamental frequency of the frequency spectrum along the associated image directions yields a filtered frequency spectrum. This filtering suppresses DC signal components and ripple, which improves signal quality. Subsequent inverse transformation of the filtered frequency spectrum to the spatial domain yields the desired phases, to within factors of integral multiples of 2xcfx80, which will be largely free of effects due to the other image direction. Eliminating the 2xcfx80 phase jumps allows deriving the relative phases along the image directions, which are a measure of the distortion components.
Phase discontinuities at the perimeter of the image field may lead to frequencies that are not actually present in the moirxc3xa9 fringe pattern and thus to analytical errors that may affect the entire image field. In order to avoid these phase discontinuities and eliminate any dependence of the results obtained on the particular shape of the, usually circular, image to be measured, under a preferred embodiment of the method, the moirxc3xa9 fringe pattern present in an image field is continuously extrapolated into a, preferably square, analysis zone surrounding the image field. The original moirxc3xa9 fringe pattern detected is inserted into this continuously extrapolated image in the form of a partial image, yielding image information that is readily analyzable in an analysis window whose central portion is largely taken up by the original moirxc3xa9 fringe pattern detected that has been continuously extrapolated outward to the perimeter of the analysis window. An algorithm that may be employed for this purpose is known as the xe2x80x9cGerchberg algorithm,xe2x80x9d and is described in the article C. Roddier and F. Roddier: xe2x80x9cInterferogram analysis using Fourier transform techniques,xe2x80x9d Applied Optics 26, 9 (1987). A variation thereon that has been optimized for use with the invention will be described in detail below in conjunction with the description of sample applications.
Another embodiment of the method effects an improvement in signal/noise ratio by superimposing at least two, temporally consecutively detected, moirxc3xa9 fringe patterns to form an additive moirxc3xa9 fringe pattern and using this additive moirxc3xa9 fringe pattern as a basis for further analysis.
Since it is to be expected that the method""s residual systematic analytical errors will vary periodically with the initial phase, a preferred embodiment of the method involves employing moirxc3xa9 fringe patterns having at least two, differing, initial phases, phase relations, or relative locations between the object and image patterns for determining individual phase distributions, detecting these, at least two, moirxc3xa9 fringe patterns, and subsequently averaging them over these individual phase distributions. Averaging over, for example, four phase intervals employing, ideally, increments of xcfx80/2, has proven adequate. However, it may also be beneficial to average over a larger number of phase intervals, for example, 8, 16, or 32 phase intervals, and employ correspondingly smaller increments, which will allow avoiding phase-related analytical errors.
The method""s spatial resolution may be improved by employing a two-dimensional detector having a two-dimensional array of rows and columns of image sensors for detecting moirxc3xa9 fringe patterns arranged with respect to the moirxc3xa9 fringe pattern such that the fringes of the moirxc3xa9 fringe pattern are oriented transversely to, in particular, run diagonally across, the rows and columns of image sensors, which will allow achieving spatial resolutions better than the detector""s nominal spatial resolution, which, for this type of detector, is given by the vertical separation of neighboring image sensors, in a simple manner.
The aforementioned and other characteristics of the invention are as stated in the accompanying claims, description, and figures, where those individual characteristics depicted may represent themselves alone or several such in the form of combinations of subsets thereof that appear in an embodiment of the invention and have been implemented in other fields, as well as beneficial embodiments that may alone be individually patentable.